# It’s All Relative: Key Ideas and Common Misconceptions About Ratio and Proportion, Grades 6-7

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## Quick Overview

For years, students have been taught to cross multiply when
presented with proportion problems. Few understand what they were doing or why
they were doing it. Rarely were students invited to think about various
representations to determine the relationship between the two ratios being
understanding of ratios and proportional thinking that is essential for solving
real-world problems and achieving success in higher-level mathematics. The
authors particularly emphasise how to use visual models to represent ratios and
proportional thinking. These visual models, which may be new to many teachers,
enhance students' conceptual understanding and improve ability to solve a wide
range of proportional reasoning problems.

For years, students have been taught to cross multiply when presented with proportion problems. Few understand what they were doing or why they were doing it. Rarely were students invited to think about various representations to determine the relationship between the two ratios being compared. The ideas and activities in this guide will help you provide students with the conceptual understanding of ratios and proportional thinking that is essential for solving real-world problems and achieving success in higher-level mathematics.

It’s All Relative includes thirty modules, which are aligned to specific Common Core State Standards. Each module in this accessible, spiral-bound flipchart:

• addresses specific mathematical practices and common misconceptions
• features timely classroom examples
• provides ideas for adapting activities to meet the needs of individual learners.

The authors particularly emphasise how to use visual models – tables, tape diagrams, graphs and double number lines – to represent ratios and proportional thinking. These visual models, which may be new to many teachers, enhance students’ conceptual understanding and improve ability to solve a wide range of proportional reasoning problems.